2022 MMATHS Problems/Problem 1: Difference between revisions
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=Problem= | ==Problem== | ||
Suppose that <math>a+b = 20, b+c = 22,</math> and <math>a+c = 2022</math>. Compute <math>\frac {a-b}{c-a}</math>. | Suppose that <math>a+b = 20, b+c = 22,</math> and <math>a+c = 2022</math>. Compute <math>\frac {a-b}{c-a}</math>. | ||
Revision as of 19:54, 18 December 2022
Problem
Suppose that 
and 
. Compute 
.
Solution 1
We solve everything in terms of 
. 
and 
. Therefore, 
. Solving for , we get that = 1010. Since 
. Since 
. Computing 
gives us the answer of 
.
~Arcticturn
